Question
Thu April 05, 2012 By: Deepshikha

Q- The traffic light at a certain road is set in the following fashion. It starts green at 06:00 and continues to be green till 06:02 and again turns green at 06:06 and continues green till 06:08. This cycle is repeated throughout the day. What percentage of the item during any given hour, the traffic light will be green? If your arrival time at this crossing is random and uniform over the interval 16:55 to 17:05, what is the probability that you will have to stop at this light?

Expert Reply
Sat April 21, 2012
The traffic light starts green at 06.00 for 2 min and is then red for next 4 min. So, the light turns green after every 6 min for 2 min. If we see in an hour, then the light will turn green at 06.00, 06.06, 06.12, 06.18, 06.24, 06.30, 06.36, 06.42, 06.48, 06.54. So, in an hour,the light will turn green 10 times for 2 min each time. Hence, a total of 20 min in 60 min(1 hour). Hence, the percentage of time in an hour, the light will be green is (20/60)*100 = 33.33%.
 
Similarly, if we see in the time frame of 16.55 - 17.05, the light will be green from 16.55 - 16.56 and then again from 17.00 - 17.02. So, out of 10 min, the light is green for 3 min and red for the rest of the 7 min. Given that your arrival time is random and uniform over this time frame, the probability that you will have to stop at this light is (7/10)*100 = 70%. 
 
Thank you
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